Method for optimizing irrigation in cultivated fields using a water gun with high flow rate

ABSTRACT

A method of optimizing the delivery of water to cultivated fields by means of a pivoting irrigation gun mounted on a moving carriage, the method consisting, for irrigating a field of length (L) and of width equal to twice the throw (P) of the gun: 
     in subdividing the irrigation zone into three successive zones, namely: a start-of-irrigation zone (Z D ), an intermediate zone (Z I ), and an end-of-irrigation zone (Z F ); and 
     in irrigating the start-of-irrigation zone (Z D ) and/or the end-of-irrigation zone (Z F ) by performing at least one alternation of a pause during which the carriage is stationary and a displacement of the carriage at a predetermined speed over a distance corresponding to one throw of the gun, so as to optimize the delivery of water relative to the delivery supplied in the intermediate zone, by limiting the water deficits (d 1 , d 2 ) at the beginning and at the end of irrigation.

The present invention relates to a method of optimizing water delivery to cultivated fields by means of a high flow rate water gun.

One of the techniques used for delivering water to large cultivated fields consist in using a high flow rate water gun pivotally mounted on a moving carriage. The gun is connected to the free end of a hose connected to a water supply source. The hose is initially wound on the support drum of a winder and a certain length thereof is unwound, after which the drum of the winder is caused to rotate so as to wind in the hose progressively, thereby pulling the carriage at substantially constant speed towards the winder while the gun delivers water by making successive sweeps over an angular sector of radius equal to the throw of the gun. In this way, it is theoretically possible to irrigate a field or a portion of a field over a length that is substantially equal to the length of the unwound hose and over a width corresponding to twice the throw of the gun.

The rate at which the hose is wound onto the drum of the winder or the travel speed of the carriage carrying the gun is determined as a function of the quantity of water that is to be delivered, which in turn is a function of the delivery rate of the gun.

A drawback inherent to that irrigation technique lies in insufficient water being delivered at the beginning and at the end of irrigation, even though an intermediate zone of the field receives overall the desired amount of water delivery. In the ideal case, the area that is irrigated would correspond to the area of the field that is to be irrigated, and also the area irrigated would receive water delivery that is as uniform as possible.

The object of the invention is to optimize this irrigation technique so as to minimize the deficit in water delivery at the beginning and at the end of irrigation, i.e. so as to tend towards the ideal of uniform water delivery over the entire irrigated area.

To this end, the invention provides a method of optimizing water delivery to cultivated fields by means of a high flow rate water gun, the method consisting in connecting the gun to the free end of a hose connected to a water supply source, in mounting the gun to pivot on a moving carriage, in unwinding the hose over a certain length from the drum of a winder so as to enable the gun to be moved away, and in rotating the drum so as to wind the hose in progressively and displace the carriage towards the drum while the gun is delivering water by performing successive sweeps over an angular sector of radius equal to one gun throw, the method being characterized in that it consists, for irrigating a field of length L and of width equal to twice the throw P of the gun:

in subdividing the irrigation zone into three successive zones, namely: a start-of-irrigation zone, an intermediate zone where the gun travels at a reference speed V_(e) corresponding to the desired water delivery, and an end-of-irrigation zone; and

in irrigating the start-of-irrigation zone and/or the end-of-irrigation zone by performing at least one alternation of a pause during which the carriage is stationary and a displacement of the carriage at a predetermined speed over a distance corresponding to one throw of the gun, or possibly vice versa in the end-of-irrigation zone, so as to optimize water delivery compared with the delivery supplied in the intermediate zone, i.e. so that the supply of water is as uniform as possible over the entire irrigated area.

In general, in order to limit water deficit in the start-of-irrigation zone, the method consists in performing alternations of pauses and displacements, such that:

the duration of each pause T_(i) is defined using the equation: $T_{i} = {\frac{{2\left( {n - i} \right)} + 1}{2n} \times \frac{P}{V_{e}}}$

where:

i lies in the range [1,n];

n is the integer number of possible alternations, and is such that n=the integer portion of (V_(max)/V_(e));

V_(max) is the maximum speed at which the hose can be wound in;

V_(e) is the reference speed of displacement for the carriage corresponding to the desired water delivery;

P is the throw of the gun; and

each displacement speed V_(i) of the carriage, after a pause, is defined from the equation:

V _(i) =n/i×V _(e)

While the start-of-irrigation zone is being irrigated under the above-specified conditions, the gun can be pointed in the travel direction of the carriage or in an opposite direction.

In general, in order to limit water deficit in the end-of-irrigation zone, the method consists in performing alternations of pauses and displacements or vice versa, such that:

the duration of each pause T_(i) is defined by the equation: $T_{i} = {\frac{{2i} - 1}{2n} \times \frac{P}{V_{e}}}$

and each displacement speed V_(i) of the carriage after a pause is defined by the equation: $V_{i} = {\frac{n}{\left( {n - i + 1} \right)} \times V_{e}}$

Specifically, the end-of-irrigation zone can be irrigated using various different approaches.

In a first approach, the method consists in performing alternations of pauses and displacements, the gun being pointed in the displacement direction of the carriage during the pauses and in the opposite direction during the displacements of the carriage, the carriage being displaced all the way to the end of the end-of-irrigation zone.

In this first approach and in order to tend towards uniform water delivery over the entire irrigated area, the start-of-irrigation zone and the intermediate zone are irrigated by pointing the gun in the opposite direction to the carriage displacement direction. In which case, the winder is placed at one end of the field, and the hose is unwound over a length (L−P) so as to position the carriage at the distance of one gun throw from the other end of the field.

In a second approach, the method consists in causing the end-of-irrigation zone to begin at (n+1) gun throws from the end of the field, in causing the carriage to be displaced at a speed (V₁) during the first throw, then causing alternations of displacements and pauses (V₂, T₁; V₃, T₂; . . . , V_(n), T_(n−1)) to be performed, the gun pointing in the displacement direction of the carriage during the displacements thereof and in an opposite direction during the pauses, and in terminating by a pause (T_(n)) once the carriage has reached one gun throw from the end of the end-of-irrigation zone with the gun pointing in the carriage displacement direction.

In this second approach and in order to tend towards uniform water delivery over the entire irrigated area, the start-of-irrigation zone and the intermediate zone are irrigated by pointing the gun in the carriage displacement direction. In which case, the winder is placed at a distance of one gun throw from one end of the field, and the hose is unwound to a length of (L−P) so as to position the carriage at the other end of the field.

In a third approach that is valid only if n is not less than 2, the method consists in performing alternations of displacements and pauses (V₁, T₁; V₁, T₂; . . . ; V_(n), T_(n)) the gun being pointed in the direction opposite to the displacement direction of the carriage both during the displacements thereof and during the pauses, while the displacement of the carriage during the first alternation takes place with the gun pointing in the displacement direction of the carriage, the displacement speeds (V₁ and V₂) during the first two alternations being such that: $V_{1} = {V_{2} = {\frac{2n}{n - 1} \times V_{e}}}$

At the end of irrigation, the gun is situated at the end of the end-of-irrigation zone.

In this third approach, and in order to tend towards uniform water delivery over the entire irrigated area, the start-of-irrigation zone and the intermediate zone are irrigated by pointing the gun in the carriage displacement direction. In which case, the winder is placed at one end of the field and the hose is unwound over a length L so as to bring the carriage to the other end of the field. This third approach gives better results than the preceding approaches, but it requires the hose to be unwound over the full length of the field, whereas the first two approaches save on a length of hose equal to one throw of the gun.

Other advantages, characteristics, and details of the invention appear from the following explanatory description made with reference to the accompanying drawings, given solely by way of example, and in which:

FIG. 1 is a diagrammatic view of a winder used in the irrigation technique mentioned in the introduction;

FIG. 2 is a perspective view showing the ideal profile for water delivery by a pivoting water gun;

FIG. 2a is a section view on line IIa—IIa of FIG. 2;

FIG. 3 is a perspective view similar to that of FIG. 2 but closer to a real irrigation profile;

FIG. 3a is a section view on line IIIa—IIIa of FIG. 3;

FIG. 4 is a diagrammatic section view to show the water delivery profile when the gun is displaced by means of a carriage along a field, while applying the irrigation technique mentioned in the introduction;

FIGS. 5a to 5 c to show the water delivery profile provided by the gun in the start-of-irrigation zone of a field when applying the method of the invention; and

FIGS. 6a to 6 d, 7, and 8 show the water delivery profile in the end-of-irrigation zone of a field in application of three different approaches of the method of the invention.

The irrigation technique mentioned in the introduction is implemented by a system as shown in FIG. 1. A water gun 1 is pivotally mounted on a carriage 3 and is connected to the end of a hose 5 which is wound onto the drum support of a winder 7 which is itself carried on a trailer 9, for example. The other end of the hose 5 is connected to a water supply and a turbine unit 10 as fixed on the trailer 9 is interposed.

With the carriage 3 assumed to be stationary, the pivoting water gun can deliver water in successive sweeps over an angular sector covering an angle of up to 230° and of radius equal to the throw of the gun 1, as shown in idealized manner in FIGS. 2 and 2a. The irrigated zone Z is assumed overall to receive the same quantity of water to a depth h₀, given that a water deficit is inevitable in the corner zones Z₁ and Z₂.

In reality, the water delivery profile as actually obtained is closer to that shown in FIGS. 3 and 3a where there can be seen a water deficit d₁ at the start of the irrigated zone Z, in addition to the deficit in the corner zones Z₁ and Z₂.

Specifically, to irrigate a field that is substantially rectangular, of length L, and of width equal to twice the throw P of the gun 1, the hose is unwound over a length (L−P) so as to position the carriage at a point P₁ situated at a distance of one throw of the gun from the other end P₀ of the field, and thereafter the winder 7 is rotated so as to pull the carriage towards the winder and as far as the winder while the gun delivers water in successive sweeps by being pointed in a direction opposite to the direction in which the carriage is displaced, i.e. the angular sector irrigated by the gun is situated behind the carriage relative to the displacement direction of the carriage.

The water delivery profile in the irrigated zone Z using that technique is illustrated in FIG. 4, and it can be seen that this irrigated zone Z can be subdivided into three successive zones:

a start-of-irrigation zone Z_(D) which extends over one throw P of the gun and in which there is a water deficit d₁ compared with the desired amount of water delivery which corresponds to a depth h₀;

an intermediate zone Z_(I) which receives overall the desired amount of water to a depth h₀; and

an end-of-irrigation zone Z_(F) extending over one gun throw and for which there is a water deficit d₂ relative to the desired amount of water delivery.

The profile shown in FIG. 4 could also be obtained if the gun were to be pointed in the same direction as the direction in which the carriage moves, i.e. if the angular sector irrigated by the gun were situated ahead of the carriage relative to the carriage displacement direction. Under such circumstances, the carriage must begin irrigation by being positioned at one end of the field.

To mitigate the water deficit d₁ in the start-of-irrigation zone Z_(D), the irrigation method of the invention can be implemented using an irrigation system of the type shown diagrammatically in FIG. 1.

In general, the method consists in alternating between pauses and displacements (T₁, V₁; T₂, V₂; . . . , T_(n), V_(n)) within the start-of-irrigation zone Z_(D) so as to ensure that:

the duration of each pause T_(i) is defined using the equation: $\begin{matrix} {T_{i} = {\frac{{2\left( {n - i} \right)} + 1}{2n} \times \frac{P}{V_{e}}}} & (1) \end{matrix}$

where:

i lies in the range [1,n];

n is the integer number of possible alternations, and is such that n= the integer portion of (V_(max)/V_(e));

V_(max) is the maximum speed at which the hose can be wound in;

P is the throw of the gun;

V_(e) is the reference speed of displacement for the carriage corresponding to the desired water delivery; and

each displacement speed V_(i) of the carriage, after a pause, is defined from the equation:

V _(i) =n/i×V _(e)  (2)

FIG. 5a shows the water delivery profile obtained in the start-of-irrigation zone Z_(D) by applying the irrigation method of the invention using a single alternation of pause and displacement (n=1). Initially, the carriage is positioned at the point P₁ situated at the distance of one gun throw from the end of the field which is marked as point P₀, and the gun is pointed in the opposite direction to the carriage displacement direction.

By convention, the direction of the arrows situated above the parameters V and T in the drawings show the direction in which the gun is pointing, given that the displacement direction of the carriage is always from left to right in the drawings.

With the carriage stationary at point P₁, a pause T₁ is implemented such that T₁=½(P/V_(e)), giving the parameters n and i the value 1 in equation (1) so as to provide a first delivery of water between the points P₀ and P₁. Once this pause T₁ has elapsed, the carriage is moved at the speed V₁=V_(e), while giving the parameters n and i the value 1 in equation (2), and it is moved over a distance equal to the throw P of the gun so as to reach point P₂. During this displacement, the gun delivers additional water between the points P₀ and P₁, and begins to deliver water between the points P₁ and P₂. As from point P₂, the carriage is displaced at the speed V_(e) so as to deliver additional water between the points P₁ and P₂ up to the depth h₀, and so as to deliver water to the depth h₀ throughout the intermediate zone Z_(I).

An examination of FIG. 5a shows that the water deficit d₁ of FIG. 4 has been greatly reduced at the beginning of the start-of-irrigation zone Z_(D), but that too much water has been delivered at the end of the start-of-irrigation zone.

The irrigation method of the invention is such that the water delivered in the deficit zones at the start of irrigation Z_(D) and at the end of irrigation Z_(F) is equal to ±(1/2)×h₀.

Thus, by performing only one pause and displacement alternation (n=1), the water delivered in the start-of-irrigation zone Z_(D) varies over a depth (±h₀/2) relative to the desired depth h₀.

It should also be observed that the start-of-irrigation zone Z_(D) is shown in FIG. 5a for the case when one alternation extends between the points P₀ and P₂, unlike the case shown in FIG. 4 where it extends between the points P₀ and P₁. The start-of-irrigation zone Z_(D) extends over a length which is multiple of the throw P of the gun and is such that:

Z _(D)=(n+1)×P

in order to limit the deficit d₁ in water delivery in said start-of-irrigation zone Z_(D).

The water delivery profile using two alternations is shown in FIG. 5b (n=2).

The carriage is stopped at point P₁ for a first pause T₁=(3/4) (P/V_(e)), giving the parameter n the value 2 and the parameter i the value 1 in equation (1), so as to begin delivering water between the points P₀ and P₁. Thereafter, the carriage is displaced at the speed V₁=2×V_(e) with i=1, and n=2 in equation (2), over a distance corresponding to one throw of the gun so as to bring the carriage to point P₂, thereby delivering additional water between points P₀ and P₁, and beginning to deliver water between points P₁ and P₂. When the carriage reaches point P₂, a second pause is performed T₂=(1/4) (P/V_(e)) to continue delivering water between the points P₁ and P₂. After this pause, the carriage is again displaced at a speed V₂=V_(e) over a distance equal to the throw P of the gun so as to bring the carriage to point P₃, thereby delivering additional water between the points P₁ and P₂, and beginning to deliver water between the points P₂ and P₃. Thereafter, the carriage is displaced at the reference speed V_(e) so as to finish off delivering water between the points P₂ and P₃ and so as to deliver water to the desired depth h₀ in the intermediate zone Z_(I).

In this way, by performing two pause-and-displacement alternations, it can be seen that the water delivered in the start-of-irrigation zone Z_(D) varies only over a depth of ±h₀/4 relative to the desired depth of water h₀, i.e. that the maximum difference has been reduced by 50% compared to the case where only one pause-and-displacement alternation is performed.

The water delivery profile using three alternations is shown in FIG. 5c (n=3).

In this case, a first pause is performed T₁=(5/6) (P/V_(e)) at point P₁, a first displacement of the carriage is performed at V₁=3V_(e) between the points P₁ and P₂, a second pause is performed T₂=(3/6) (P/V_(e)) at point P₂, the carriage is displaced a second time at a speed V₂=(3/2) (V_(e)) between the points P₂ and P₃, a third pause is performed T₃=(1/6) (P/V_(e)) at the point P₃, and the carriage is moved a third time at a speed V₃=V_(e) between the points P₃ and P₄.

With three alternations, the water delivered in the start-of-irrigation zone Z_(D) varies by no more than a depth of ±h₀/6 relative to the desired depth of water h₀. In other words, the greater the number of alternations, the more the delivery of water in the start-of-irrigation zone Z_(D) is optimized, it nevertheless being understood that this number n has a limit value which depends on the maximum speed V_(max) at which the carriage can move.

The explanations given above remain unchanged if, at the beginning of irrigation, the gun points in the displacement direction of the carriage. This variant is represented by the dashed line arrows in FIG. 5a, it being understood that the gun then needs to be placed at the end of the field and not at one gun throw from said end.

To mitigate the water deficit d₂ in the end-of-irrigation zone Z_(F) of the field to be irrigated, the irrigation method of the invention consists in alternating pauses and displacements, or vice versa, such that:

the duration of each pause T_(i) is defined by the equation: $\begin{matrix} {T_{i} = {\frac{{2i} - 1}{2n} \times \frac{P}{V_{e}}}} & (2) \end{matrix}$

and each displacement speed V_(i) of the carriage after a pause is defined by the equation: $\begin{matrix} {V_{i} = {\frac{n}{\left( {n - i + 1} \right)} \times V_{e}}} & (4) \end{matrix}$

The delivery of water in the end-of-irrigation zone Z_(F) can be performed using various approaches.

In a first approach, alternating pauses and displacements (T₁, V₁; T₂, V₂; . . . , T_(n), V_(n)) are performed and it is assumed that the intermediate zone Z_(I) has been irrigated with the gun pointing in the opposite direction to the displacement direction of the gun. In this first approach, the end-of-irrigation zone Z_(F) begins at n throws P before the end of the field. The water delivery profile obtained using three alternations is illustrated in FIGS. 6a to 6 d (n=3). In this example, the end-of-irrigation zone Z_(F) begins at point P₁ which is situated at a distance of three throws P defined between points P₁, P₃, P₃, and P₄, measured from the end of the field which is defined by the point P₄.

When the carriage reaches the point P₁, a first pause T₁ of duration (1/6) (P/V_(e)) is performed, giving the parameter n the value 3 and the parameter i the value 1 in equation (3), with the gun pointing in the displacement direction of the carriage (FIG. 6a) so as to begin delivering water between points P₁ and P₂. Thereafter, the carriage is displaced from point P₁ to point P₂ at a speed V₁=V_(e), giving the parameter n the value 3 and the parameter i the value 1 in equation (4), with the gun pointing in the direction opposite to the displacement direction of the carriage so as to continue delivering water between the points P₁ and P₂ (FIG. 6b). When the carriage reaches point P₂, a second pause is performed for a duration T₂=(3/6)/(P/V_(e)) giving the parameter n the value 3 and the parameter i the value 2 in equation (3), and pointing the gun in the displacement direction of the carriage (FIG. 6b) so as to begin delivering water between the points P₂ and P₃. The carriage is then displaced from point P₂ to point P₃ at a speed V₂=(3/2)/(V_(e)), giving the parameter n the value 3 and the parameter i the value 2 in equation (4), and pointing the gun in the direction opposite to the displacement direction of the carriage so as to finish off delivering water between the points P₁ and P₂ and so as to continue to bring water between the points P₂ and P₃. When the carriage reaches the point P₃, a third pause of duration T₃=(5/6) (P/V_(e)) is performed giving the parameters n and i the value 3 in equation (3), and pointing the gun in the carriage displacement direction (FIG. 6c) so as to begin delivering water between the points P₃ and P₄. Finally, the direction in which the gun is pointing is reversed and the carriage is displaced from point P₃ to point P₄ marking the finish of the end-of-irrigation zone Z_(F) at a speed V₃=3V_(e) (FIG. 6d), giving the parameters n and i the value 3 in equation (4), so as to finish off delivering water between the points P₂ and P₄.

In this first approach for mitigating the water deficit d₂ in the end-of-irrigation zone Z_(F) of the field, the gun always points in the carriage displacement direction during the pauses and in the opposite direction while the carriage is moving, it being understood that the intermediate zone of the field has already been irrigated with the gun pointing in the direction opposite to the displacement direction of the carriage.

With three pause-and-displacement alternations, the delivery of water in the end-of-irrigation zone Z_(F) varies only over a depth of ±h₀/6 relative to the desired depth of water h₀, whereas the variation would have been ±h₀/4 if two alternations had been performed.

Thus, in order to tend towards uniform delivery of water over the entire irrigated area by applying this first approach, the start-of-irrigation zone Z_(D) and the intermediate zone Z_(I) are irrigated with the gun pointing in the direction opposite to the displacement direction of the carriage. Under such circumstances, the winder is placed at one end of the field, and the hose is unwound at the beginning of irrigation for a length (L−P) so as to position the carriage at a distance of one gun throw from the other end of the field. Under such conditions, the method makes it possible to limit the water deficit d₁ and d₂ in the start-of-irrigation zone and in the end-of-irrigation zone, and to deliver a little water into the corner zones Z₁ and Z₂ situated in the end-of-irrigation zone Z_(F).

In a second approach, the method consists in causing the end-of-irrigation zone (Z_(F)) to begin at (n+1) gun throws from the end of the field, in causing the carriage to move at the speed (V₁) in the first throw, then in performing alternating displacements and pauses (V₂, T₁; V₃, T₂; . . . , V_(n), T_(n−1), the gun pointing in the displacement direction of the carriage during displacements thereof and in an opposite direction during pauses, and in terminating with a pause (T_(n)) when the carriage has reached one gun throw from the end of the end-of-irrigation zone, with the gun pointing in the displacement direction of the carriage. The water delivery profile obtained with three alternations is illustrated in FIG. 7.

The end-of-irrigation zone Z_(F) begins at the point P₁ which is situated at a distance of four throws P, as defined between the points P₁ to P₅, from the end of the field which is defined by the point P₅.

On reaching the point P₁, the carriage is displaced at a speed V₁=V_(e), giving the parameter n the value 3 and the parameter i the value 1 in equation (4) so as to finish off delivering water between the points P₁ and P₂ and so as to begin delivering water between the points P₂ and P₃. From point P₂, the carriage is displaced at a speed V₂=(3/2) (V_(e)) giving the parameter n the value 3 and the parameter i the value 2 in equation (4), to continue delivering water between the points P₂ and P₃, and to begin delivering water between the points P₃ and P₄. At point P₃, the carriage is caused to stand still and a first pause is performed on duration T₁=(1/6) (P/V_(e)), giving the parameter n the value 3 and the parameter i the value 1 in equation (3), and reversing the direction in which the gun points so as to finish off delivering water between the points P₂ and P₃. The carriage is then moved from point P₃ to point P₄ at a speed V₃=3×V_(e), giving the parameters n and i the value 3 in equation (4) and pointing the gun in the displacement direction of the carriage so as to continue delivering water between the points P₃ and P₄, and begin delivering water between the points P₄ and P₅. At point P₄, the carriage is stopped and a second pause of duration T₂=(3/6) (P/V_(e)) is performed, giving the parameter n the value 3 and the parameter i the value 2 in equation (3), and reversing the direction in which the gun points so as to finish off delivering water between the points P₃ and P₄. Finally, with the carriage still stationary at the point P₄, a third pause of duration T₃=(5/6) (P/V_(e)) is performed, giving the parameters n and i the value 3 in equation (3), with the direction in which the gun is pointing being reversed so as to finish off delivering water between the points P₄ and P₅.

In this example, it will be observed that the carriage has not gone all the way to the point P₅ marking the finish of the end-of-irrigation zone Z_(F), but has been stopped at point P₄ which is situated at a distance of one gun throw from the point P₅.

In this second approach for mitigating the water deficit d₂ in the end-of-irrigation zone Z_(F) of the field, the gun always points in a displacement direction of the carriage while it is being displaced, and the gun points in the opposite direction to the displacement direction of the carriage during the first (n−1) pauses.

With three displacement-and-pause alternations, the delivery of water in the end-of-irrigation zone Z_(F) varies only by a depth of (±h₀/6) relative to the desired depth of water h₀, whereas the variation would have been (±h₀/4) if only two alternations had been performed.

Thus, in order to tend towards uniform delivery of water over the entire irrigated area by applying this second approach, the start-of-irrigation zone and the intermediate zone are irrigated with the gun pointing in the displacement direction of the carriage. Under such circumstances, the winder is placed at a distance of one gun throw from one end of the field, and the hose is unwound over a length (L−P) so as to position the carriage at the other end of the field. Under such conditions, the method makes it possible to limit water deficits d₁ and d₂ in the start-of-irrigation zone and the end-of-irrigation zone of the field, and enables a medium delivery of water to be provided in the corner zones Z₁ and Z₂ situated in the start-of-irrigation zone Z_(D).

In a third approach with n equal to at least two, displacement and pause alternations (V₁, T₁; V₂, T₂; . . . , V_(n), T_(n)) are performed, and it is assumed that the intermediate zone Z₁ is irrigated with the gun pointing in the displacement direction of the carriage. The water delivery profile obtained with three alternations is shown in FIG. 8 (n=3).

The end-of-irrigation zone Z_(F) begins at point P₁ which is situated at a distance of n throws P from the end of the field as defined by a point P₄, i.e. it is at a distance of three throws defined between the points P₁ and P₄.

On reaching point P₁, the carriage is moved at speed V₁ so as to continue delivering water between the points P₁ and P₂ and so as to begin delivering water between the points P₂ and P₃.

This speed V₁ is such that: $V_{1} = {{\frac{2n}{n - 1} \times V_{e}} = {3 \times V_{e}}}$

The carriage is stopped at point P₂ and a first pause T₁ is performed to continue delivering water between the points P₁ and P₂ with the direction in which the gun is pointing being reversed. Thereafter, the carriage is moved from point P₂ to point P₃ at a speed V₂=V₁=3×V_(e) to finish off delivering water between the points P₁ and P₂, and to continue delivering water between the points P₂ and P₃, the gun continuing to point in the opposite direction to the carriage displacement direction until the end of irrigation. The carriage is stopped at point P₃ and a second pause T₂ is performed to continue to deliver water between the points P₂ and P₃, and then the carriage is displaced to point P₄ at the speed V₁=3×V_(e) so as to finish off delivering water between the points P₂ and P₃, and so as to begin delivering water between the points P₃ and P₄. Finally, a last pause T₃ is performed so as to finish off delivering water between the points P₃ and P₄.

With three pause-and-displacement alternations, the delivery of water in the end-of-irrigation zone Z_(F) varies only over a depth of ±h₀/6 relative to the desired depth of water h₀, whereas the variation would have been ±h₀/4 if only two alternations were performed.

Thus, in order to tend towards uniform delivery of water over the entire irrigated area by applying this third approach, the start-of-irrigation zone Z_(D) and the intermediate zone Z_(I) are irrigated with the gun pointing in the opposite direction to the displacement direction of the carriage. In this case, the winder is placed at one end of the field and the hose is unwound at the beginning of irrigation over the entire length L of the field so as to position the carriage at the other end of the field. Overall, the same results are obtained as with the second approach, but in addition, the corner zones Z₁ and Z₂ of the start-of-irrigation zone Z_(D) are also properly irrigated, however the hose has to be unwound over the entire length that is to be irrigated, i.e. there is no saving of a length of hose equal to the throw of the gun.

The method of the invention leads to several conclusions.

A first conclusion is that the trend towards water delivery that is as uniform as possible over the entire length of a field increases with increasing value for the parameter n. The first pause T₁ in the start zone Z_(D) and the last pause Tn in the end zone Z_(F) tend towards the value (P/V_(e)) which corresponds to the desired depth of water delivery h₀ while the carriage is traveling one throw P at the speed V_(e) in the intermediate zone Z_(I).

A second conclusion is that the variations of ±h₀/2n in the delivery of water in the start and end zones Z_(D) and Z_(F) relative to the desired depth of water h₀ tend towards the value zero as the value of the parameter n tends towards infinity.

A third conclusion is that using the above-specified formulae specifying the duration of the pauses and the speeds of irrigation in the start zone Z_(D) and in the end zone Z_(F), it can be shown that the additional durations of irrigation in these zones Z_(D) and Z_(F) compared with the duration of irrigation if the method is not applied, are constant whatever the value of the parameter n, and each is equal to (1/2) (P/V_(e)) (where P is the length of one gun throw, and V_(e) is the reference speed of irrigation in the intermediate zone Z_(I) for obtaining the desired delivery of water to the depth h₀).

With reference to the start zone Z_(D), it has been shown that for iε[1,n]:

the i^(th) pause has a duration T_(i) such that: $T_{i} = {\frac{{2\left( {n - i} \right)} + 1}{2n} \times \frac{P}{V_{e}}}$

the i^(th) irrigation speed V_(i) is such that:

V _(i) =n/i×V _(e)

As a result the duration D_(i) for traveling over one throw P at the irrigation speed V_(i) is such that: $D_{i} = {\frac{i}{n} \times \frac{P}{V_{e}}}$

Consequently, the total duration D_(D) of irrigation in the start zone Z_(D) is such that: $D_{D} = {{\sum\limits_{i = 1}^{n}\left( {T_{i} + D_{i}} \right)} = {\left( {n + \frac{1}{2}} \right) \times \frac{P}{V_{e}}}}$

Given that the length of the start zone that is processed for compensating water deficit is equal to (n+1)×P, but with the carriage being displaced through n throws only, the supplementary duration D_(S) of irrigation compared with the duration of irrigation without applying the method over the same length irrigated at the speed V_(e) is equal to: $D_{S} = {{\left( {n + \frac{1}{2}} \right) \times \frac{P}{V_{e}}} - \frac{n \times P}{V_{e}}}$ $D_{S} = {\frac{1}{2} \times \frac{P}{V_{e}}}$

A similar calculation can be done to show that the supplementary duration of irrigation in the end zone Z_(F) is also equal to (1/2) (P/V_(e)) whichever approach is used.

A fourth conclusion that can be drawn from the preceding conclusion is that the total duration D_(T) of irrigation of a field of length L when the method of the invention is applied is constant, whatever the value of the parameter n and is equal to: $D_{T} = \frac{L}{V_{e}}$

Specifically:

the total duration D_(T) of irrigation of the same field without applying the method is equal to: $D_{T} = \frac{L - P}{V_{e}}$

since the gun is unwound over a length L−P, and

the supplementary duration of irrigation of the same field when the method is applied is equal to 2×(1/2) (P/V_(e)).

In other words, the total duration of irrigation using the method of the invention is indeed: $D_{T} = {{\frac{L - P}{V_{e}} + \frac{P}{V_{e}}} = \frac{L}{V_{e}}}$

Above, the method of the invention has been applied under the following conditions:

the maximum speed of the carriage which carries the water gun or the maximum speed of the hose winder is equal to n times the irrigation speed V_(e) corresponding to a desired water throw; and

the parameter n is the integer part of the ratio V_(max)/V_(e).

We consider the application of the method of the invention to compensating water deficit in the start zone Z_(D). ${{1/\quad {If}}\quad 2} \leq \frac{V_{\max}}{V_{e}} < 3$

Then, as shown in FIG. 5b, the parameter n has the value 2 and the following sequence is applied: ${T_{1} = {\frac{3}{2} \times \frac{P}{V_{e}}}};{V_{1} = {2V_{e}}};{T_{2} = {\frac{1}{4} \times \frac{P}{V_{e}}}}$

with variations in water delivery of (±h₀/4). ${{2/\quad {If}}\quad 3} \leq \frac{V_{\max}}{V_{e}} < 4$

Then, as shown in FIG. 5c, the parameter n is given the value 3 and the following sequence is applied: ${T_{1} = {\frac{5}{6} \times \frac{P}{V_{e}}}};{V_{1} = {3V_{e}}};{T_{2} = {\frac{3}{6} \times \frac{P}{V_{e}}}};{V_{2} = {\frac{3}{2}\quad V_{e}}};{T_{3} = {\frac{1}{6} \times \frac{P}{V_{e}}}}$

with variations in water delivery of (±h₀/6).

It is then possible to improve the method of the invention as described above by seeking to determine the irrigation speed lying in the range 2V_(e) to 3V_(e) (for the case where n=2) from which it will be possible to apply the first pause T₁ as defined when n is equal to 3.

When n is equal to 2, the first pause T₁ is equal to (3/4) (P/V_(e)), which leads to variations in water delivery of (±h₀/4) However, when n is equal to 3, the first pause T₁ is equal to (5/6) (P/V_(e)) which leads to variations in water delivery of (±h₀/6), i.e. a closer approach is obtained to the desired water delivery in the first throw of the start zone Z_(D).

However, if it is desired to apply the first pause T₁ as defined for n=3 when the maximum irrigation speed lies in the range 2V_(e) to 3V_(e) (the case where n=2), variations in water delivery must not exceed (±h₀/4) while the carriage travels over the second throw of the start zone Z_(D) adding to the water already delivered in the first throw.

This puts a condition on the speed V_(x) that the winder can be allowed to reach, namely:

the displacement speed V_(x) applied to the carriage after the first pause T₁ is such that:

V _(e)×(n−1)<V _(xmin) ≦V _(x) <n×V _(e)

where V_(xmin), i.e. the minimum possible speed V_(x), satisfies the following formula: $V_{xmin} = {V_{e} \times 2 \times \frac{n\quad \left( {n - 1} \right)}{{2n} - 1}}$

To satisfy this condition, it is necessary for the second pause T_(x) to satisfy the following inequality: $T_{xmin} = {{\frac{\left( {{2n} - 1} \right)\quad \left( {n - 2} \right)}{2n\quad \left( {n - 1} \right)} \times \frac{P}{V_{e}}} \leq T_{x} \leq {\frac{{2n} - 3}{2n} \times \frac{P}{V_{e}}}}$

so that the carriage travels through the second throw after the irrigation duration Dn defined for the value n (T_(xmin) corresponding to the speed of T_(x) for V_(x)=V_(xmin)).

This duration of irrigation D_(n) is such that: $D_{n} = {T_{1} + \frac{P}{V_{1}} + T_{2}}$ $D_{n} = {\left\lbrack {\frac{{2n} - 1}{2n} + \frac{1}{n} + \frac{{2n} - 3}{2n}} \right\rbrack \times \frac{P}{V_{e}}}$ $D_{n} = {\frac{{2n} - 1}{n} \times \frac{P}{V_{e}}}$

However, this duration of irrigation D_(n) must be equal to: $D_{n} = {T_{1} + \frac{P}{V_{x}} + T_{x}}$

so it can be deduced that: $T_{x} = {{\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}} - \frac{P}{V_{x}}}$

Also, the value of T_(xmin) corresponds to V_(xmin) so it can be deduced that: $T_{xmin} = {{\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}} - \frac{P}{V_{xmin}}}$ $T_{xmin} = {\frac{\left( {{2n} - 1} \right)\quad \left( {n - 2} \right)}{2n\quad \left( {n - 1} \right)} \times \frac{P}{V_{e}}}$

In addition, since the value of T_(xmax) corresponds to V_(max)=nV_(e), it can be deduced that: $T_{xmax} = {{\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}} - \frac{P}{n\quad V_{e}}}$ $T_{xmax} = {\frac{{2n} - 3}{2n} \times \frac{P}{V_{e}}}$

This value for T_(xmax) does indeed correspond to the value of the second pause T₂ for the value n.

Thus, returning to the case where the maximum speed of the carriage lies in the range 2V_(e) to 3V_(e), the following are defined:

an irrigation speed V_(xmin)=(12/5)V_(e); and

a minimum duration T_(xmin)=(5/12) (P/V_(e)).

Under these conditions, when the maximum speed of the carriage lies in the range 2V_(e) to 3V_(e), and when it has a minimum value equal to (12/5)V_(e), it is possible to apply the following sequence to compensate the water deficit in the start zone Z_(D):

a first pause T₁ equal to (5/6) (P/V_(e)) which corresponds to the pause T₁ for n=3;

a speed of irrigation V₁=V_(x) which is greater than or equal to (12/5)V_(e);

a second pause T₂ greater than or equal to (5/12) (P/V_(e));

an irrigation speed V₂ equal to (3/2)V_(e) which corresponds to the speed V₂ for n=3; and

a third pause T₃ equal to (1/6) (P/V_(e)) which corresponds to the pause T₃ for n=3, i.e. the following sequence: ${T_{1} = {\frac{5}{6} \times \frac{P}{V_{e}}}};{V_{1} \geq {\frac{12}{5}\quad V_{e}}};$ ${T_{2} = {\frac{5}{12} \times \frac{P}{V_{e}}}};{V_{2} = {\frac{3}{2} \times \frac{P}{V_{e}}}};{T_{3} = {\frac{1}{6} \times \frac{P}{V_{e}}}}$

This improvement to the method of compensating water deficit in the start zone Z_(D) can be specified in terms of three rules when the maximum irrigation speed for carriage displacement or hose winding onto the winder lies in the range (n−1)V_(e) to nV_(e), for V_(e) being the speed corresponding to the desired water delivery:

Rule 1: apply the first pause T₁ corresponding to the value n, i.e.:

$T_{1} = {\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}}$

Rule 2: ensure that water delivery does not exceed that which corresponds to the value (n−1), which implies a speed V_(x) for application to the carriage after the first pause T₁ whose value lies in the range: $V_{xmin} = {{V_{e} \times 2\quad \frac{n\quad \left( {n - 1} \right)}{{2n} - 1}} \leq V_{x} < {n\quad V_{e}}}$

Rule 3: begin the displacement of the carriage for traveling over the second throw at the instant defined for the value n, which implies a second pause T_(x) whose value lies in the range: $T_{xmin} = {{\frac{\left( {{2n} - 1} \right)\quad \left( {n - 2} \right)}{2n\quad \left( {n - 1} \right)} \times \frac{P}{V_{e}}} \leq T_{x} \leq {\frac{{2n} - 3}{2n} \times \frac{P}{V_{e}}}}$

This improvement to the method as specified by the three above rules can also be applied to compensate for deficit in water delivery in the end zone Z_(F).

For the first two approaches envisaged above for the end zone Z_(F), the three rules become the following when the maximum speed of the carriage lies in the range (n−1)V_(e) and nV_(e):

Rule 1: apply the n^(th) pause T_(n) corresponding to the value n, i.e.: $T_{n} = {\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}}$

Rule 2: ensure that water delivery does not exceed that which corresponds to the value (n−1), which implies a speed V_(x) whose value must lie in the range: $V_{xmin} = {{V_{e} \times 2\quad \frac{n\quad \left( {n - 1} \right)}{{2n} - 1}} \leq V_{x} < {n\quad V_{e}}}$

Rule 3: modify only the pause corresponding to the value (n−1) so as to keep the total duration of the arrival sequence constant and such that: $T_{n - 1} = {{\frac{\left( {{2n} - 1} \right)}{2n} \times \frac{P}{V_{e}}} - \frac{P}{V_{x}}}$

When the third approach is used, the displacement speeds V₁ and V₂ during the first two alternations (n being not less than 2), are equal and such that: $V_{1} = {V_{2} = {\frac{\left( {{2n} - 1} \right)}{2n} \times V_{e}}}$

The above-stated three rules can be applied only for a value of n not less than 4 (n≧4), i.e. a speed V_(x)≧(24/7)V_(e).

For n having values of 2 and 3, the speeds V₁ and V₂ are greater than or equal to nV_(e).

In which case, the improvement will be as follows for a carriage speed V_(x) lying in the range:

4/3<V _(x)<3V _(e)

Rule 1: on beginning the end zone Z_(F), travel through the throw in the displacement direction at the speed V_(x);

Rule 2: before traveling through the second throw in the direction opposite to the displacement direction, make a pause T_(x1) equal to one-fourth of the time that remains relative to the normal duration taken to travel through the two throws in accordance with the method, i.e. at a speed of 4V_(e); and

Rule 3: at the end of traveling through the second throw, make a pause T_(x2) equal to 3T_(x1).

Finally, all of the formulae given above are based on the assumption that variation in flow rate is negligible, and regulation has been performed on the basis of time. The formulae need to be corrected by ΔT_(i) and ΔV_(i) when regulation is performed on the basis of measuring flow rate. 

What is claimed is:
 1. A method of optimizing water delivery to cultivated fields by means of a high flow rate water gun, the method consisting in connecting the gun to the free end of a hose connected to a water supply source, in mounting the gun to pivot on a moving carriage, in unwinding the hose over a certain length from the drum of a winder so as to enable the gun to be moved away, and in rotating the drum so as to wind the hose in progressively and displace the carriage towards the drum while the gun is delivering water by performing successive sweeps over an angular sector of radius equal to one gun throw, the method being characterized in that it consists, for irrigating a field of length (L) and of width equal to twice the throw (P) of the gun: in subdividing the irrigation zone into three successive zones, namely: a start-of-irrigation zone (Z_(D)), an intermediate zone (Z_(I)) where the gun travels at a reference speed (V_(e)) corresponding to the desired water delivery, and an end-of-irrigation zone (Z_(F)); and in irrigating the start-of-irrigation zone (Z_(D)) and/or the end-of-irrigation zone (Z_(F)) by performing at least one alternation of a pause during which the carriage is stationary and a displacement of the carriage at a predetermined speed over a distance corresponding to one throw of the gun, or possibly vice versa in the end-of-irrigation zone, so as to optimize water delivery compared with the delivery supplied in the intermediate zone, i.e. so that the supply of water is as uniform as possible over the entire irrigated area.
 2. A method according to claim 1, characterized in that in order to limit water deficit in the start-of-irrigation zone (Z_(D)), the method consists in performing alternations of pauses and displacements (T₁, V₁; T₂, V₂; . . . , T_(n), V_(n)), such that: the duration of each pause T_(i) is defined using the equation: $T_{i} = {\frac{{2\left( {n - i} \right)} + 1}{2n} \times \frac{P}{V_{e}}}$

 where: i lies in the range [1,n]; n is the integer number of possible alternations, and is such that n=the integer portion of (V_(max)/V_(e)); V_(max) is the maximum speed at which the hose can be wound in; V_(e) is the reference speed of displacement for the carriage corresponding to the desired water delivery; P is the throw of the gun; and each displacement speed V_(i) of the carriage, after a pause, is defined from the equation: V _(i) =n/i×V _(e)
 3. A method according to claim 2, characterized in that it consists in positioning the carriage at one gun throw from the start of the start-of-irrigation zone (Z_(D)) when the gun points in the direction opposite to the displacement direction of the carriage, or in placing the carriage at the start of the start-of-irrigation zone (Z_(D)) when the gun is pointed in the displacement direction of the carriage.
 4. A method according to claim 2, characterized in that it consists, when the maximum speed of the carriage lies in the range (n−1)V_(e) and nV_(e): in applying the first pause T₁ corresponding to the value n, i.e.: $T_{1} = {\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}}$

in ensuring that water delivery does not exceed that which corresponds to the value (n−1), which implies a speed V_(x) for application to the carriage after the first pause T₁ and whose value lies in the range: $V_{xmin} = {{V_{e} \times 2\quad \frac{n\quad \left( {n - 1} \right)}{{2n} - 1}} \leq V_{x} \leq {n\quad V_{e}}}$

in beginning the displacement of the carriage for traveling over the second throw at the instant defined for the value n, which implies a second pause T_(x) whose value lies in the range: $T_{xmin} = {{\frac{\left( {{2n} - 1} \right)\quad \left( {n - 2} \right)}{2n\quad \left( {n - 1} \right)} \times \frac{P}{V_{e}}} \leq T_{x} \leq {\frac{{2n} - 3}{2n} \times {\frac{P}{V_{e}}.}}}$


5. A method according to claim 1, characterized in that, in order to limit water deficit in the end-of-irrigation zone (Z_(F)), the method consists in performing alternations of pauses and displacements or vice versa, such that: the duration of each pause T_(i) is defined by the equation: $T_{i} = {\frac{{2i} - 1}{2n} \times \frac{P}{V_{e}}}$

and each displacement speed V_(i) of the carriage after a pause is defined by the equation: $V_{i} = {\frac{n}{\left( {n - i + 1} \right)} \times {V_{e}.}}$


6. A method according to claim 5, characterized in that it consists in performing alternations of pauses and displacements (T₁, V₁; T₂, V₂; . . . ; T_(n), V_(n)), the gun being pointed in the displacement direction of the carriage during the pauses and in the opposite direction during the displacements of the carriage, the carriage being displaced all the way to the end of the end-of-irrigation zone.
 7. A method according to claim 6, characterized in that it consists in irrigating the start-of-irrigation zone (Z_(D)) and the intermediate zone (Z_(I)) with the gun pointing in the direction opposite to the displacement direction of the carriage, and in making the end-of-irrigation zone (Z_(F)) begin at n gun throws from the end of the field.
 8. A method according to claim 5, characterized in that it consists in causing the end-of-irrigation zone (Z_(F)) to begin at (n+1) gun throws from the end of the field, in causing the carriage to be displaced at a speed (V₁) during the first throw, then causing alternations of displacements and pauses (V₂, T₁; V₃, T₂; . . . , V_(n), T_(n−1)) to be performed, the gun pointing in the displacement direction of the carriage during the displacements thereof and in an opposite direction during the pauses, and in terminating by a pause (T_(n)) once the carriage has reached one gun throw from the end of the end-of-irrigation zone with the gun pointing in the carriage displacement direction.
 9. A method according to claim 8, characterized in that it consists in irrigating the start-of-irrigation zone and the intermediate zone with the gun pointing in the displacement direction of the carriage.
 10. A method according to claim 5, characterized in that it consists, when the maximum speed of the carriage lies in the range (n−1)V_(e) to nV_(e): in applying the n^(th) pause T_(n) corresponding to the value n, i.e.: $T_{n} = {\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}}$

in ensuring that water delivery does not exceed that which corresponds to the value (n−1), which implies a speed V_(x) whose value must lie in the range: $V_{xmin} = {{V_{e} \times 2\quad \frac{n\quad \left( {n - 1} \right)}{{2n} - 1}} \leq V_{x} < {n\quad V_{e}}}$

in modifying only the pause corresponding to the value (n−1) so as to keep the total duration of the arrival sequence constant and such that: $T_{n - 1} = {{\frac{\left( {{2n} - 1} \right)}{2n} \times \frac{P}{V_{e}}} - {\frac{P}{V_{x}}.}}$


11. A method according to claim 5, characterized in that, for a number of alternations not less than 2, the method consists in performing alternations of displacements and pauses (V₁, T₁; V₁, T₂; . . . ; V_(n), T_(n)) the gun being pointed in the direction opposite to the displacement direction of the carriage both during the displacements thereof and during the pauses, while the displacement of the carriage during the first alternation takes place with the gun pointing in the displacement direction of the carriage, the displacement speeds (V₁ and V₂) during the first two alternations being such that: $V_{1} = {V_{2} = {\frac{2n}{n - 1} \times {V_{e}.}}}$


12. A method according to claim 11, characterized in that it consists in irrigating the start-of-irrigation zone (Z_(D)) and the intermediate zone (Z_(I)) with the gun pointing in the displacement direction of the carriage, and in causing the end-of-irrigation zone (Z_(F)) to begin at n throws of the gun from the end of the field.
 13. A method according to claim 9, characterized in that it consists, when the maximum speed of the carriage lies in the range (n−1)V_(e) to nV_(e) for n≧4: in applying the n^(th) pause T_(n) corresponding to the value n, i.e.: $T_{n} = {\frac{{2n} - 1}{2n} \times \frac{P}{V_{e}}}$

in ensuring that water delivery does not exceed that which corresponds to the value (n−1), which implies a speed V_(x) whose value must lie in the range: $V_{xmin} = {{V_{e} \times 2\quad \frac{n\quad \left( {n - 1} \right)}{{2n} - 1}} \leq V_{x} < {n\quad V_{e}}}$

in modifying only the pause corresponding to the value (n−1) so as to keep the total duration of the arrival sequence constant and such that: $T_{n - 1} = {{\frac{\left( {{2n} - 1} \right)}{2n} \times \frac{P}{V_{e}}} - {\frac{P}{V_{x}}.}}$


14. A method according to claim 11, characterized in that it consists, when the speed of the carriage V_(x) lies in the range (4/3)V_(e) to 3V_(e): on beginning the end zone Z_(F), in traveling through the throw in the displacement direction at the speed V_(x); before traveling through the second throw in the direction opposite to the displacement direction, in making a pause T_(x1) equal to one-fourth of the time that remains relative to the normal duration taken to travel through the two throws in accordance with the method, i.e. at a speed of 4V_(e); and at the end of traveling through the second throw, in making a pause T_(x2) equal to 3T_(x1). 